Extension theorems for differential forms and Bogomolov-Sommese vanishing on log canonical varieties

Abstract

Given a p-form defined on the smooth locus of a normal variety, and a resolution of singularities, we study the problem of extending the pull-back of the p-form over the exceptional set of the desingularization. For log canonical pairs and for certain values of p, we show that an extension always exists, possibly with logarithmic poles along the exceptional set. As a corollary, it is shown that sheaves of reflexive differentials enjoy good pull-back properties. A natural generalization of the well-known Bogomolov-Sommese vanishing theorem to log canonical threefold pairs follows.

final version with improved exposition and several minor clarifications and corrections

Cited by in corpus (17)

• Differential Forms on Log Canonical Spaces
• Smoothable del Pezzo surfaces with quotient singularities
• Codimension one foliations with numerically trivial canonical class on singular spaces
• Pull-back Morphisms for Reflexive Differential Forms
• Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities
• Families over special base manifolds and a conjecture of Campana
• The Zariski-Lipman conjecture for log canonical spaces
• The structure of surfaces and threefolds mapping to the moduli stack of canonically polarized varieties
• Algebraic approximation of Kähler threefolds of Kodaira dimension zero
• Projectively flat KLT varieties
• Differential forms on log canonical spaces in positive characteristic
• The fundamental group of compact K{ä}hler threefolds
• On the structure of homogeneous symplectic varieties of complete intersection
• Canonical surfaces with big cotangent bundle
• On Classification of compact complex surfaces of class VII
• Varieties with Ample Tangent Sheaves
• The Violation of the Lipman-Zariski conjecture in positive characteristic